Drake
Rod2D< T > Class Template Reference

Dynamical system representation of a rod contacting a half-space in two dimensions. More...

#include <drake/examples/rod2d/rod2d.h>

Inheritance diagram for Rod2D< T >:
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Collaboration diagram for Rod2D< T >:
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Public Types

enum  SystemType { kPiecewiseDAE, kDiscretized, kContinuous }
System model and approach for simulating the system. More...

Public Member Functions

~Rod2D () override

Rod2D (SystemType system_type, double dt)
Constructor for the 2D rod system using the piecewise DAE (differential algebraic equation) based approach, the discretization approach, or the continuous ordinary differential equation based approach. More...

Transforms dissipation (α) to damping, given a characteristic. More...

double TransformDampingToDissipationAboutDeformation (double characteristic_deformation, double b) const
Transforms damping (b) to dissipation (α) , given a characteristic deformation. More...

double get_cfm () const
Gets the constraint force mixing parameter (CFM, used for discretized systems only), which should lie in the interval [0, infinity]. More...

double get_erp () const
Gets the error reduction parameter (ERP, used for discretized systems only), which should lie in the interval [0, 1]. More...

Vector3< T > GetRodConfig (const systems::Context< T > &context) const
Gets the generalized position of the rod, given a Context. More...

Vector3< T > GetRodVelocity (const systems::Context< T > &context) const
Gets the generalized velocity of the rod, given a Context. More...

double get_gravitational_acceleration () const
Gets the acceleration (with respect to the positive y-axis) due to gravity (i.e., this number should generally be negative). More...

void set_gravitational_acceleration (double g)
Sets the acceleration (with respect to the positive y-axis) due to gravity (i.e., this number should generally be negative). More...

double get_mu_coulomb () const
Gets the coefficient of dynamic (sliding) Coulomb friction. More...

void set_mu_coulomb (double mu)
Sets the coefficient of dynamic (sliding) Coulomb friction. More...

double get_rod_mass () const
Gets the mass of the rod. More...

void set_rod_mass (double mass)
Sets the mass of the rod. More...

double get_rod_half_length () const
Gets the half-length h of the rod. More...

void set_rod_half_length (double half_length)
Sets the half-length h of the rod. More...

double get_rod_moment_of_inertia () const
Gets the rod moment of inertia. More...

void set_rod_moment_of_inertia (double J)
Sets the rod moment of inertia. More...

double get_stiffness () const
Get compliant contact normal stiffness in N/m. More...

void set_stiffness (double stiffness)
Set compliant contact normal stiffness in N/m (>= 0). More...

double get_dissipation () const
Get compliant contact normal dissipation in 1/velocity (s/m). More...

void set_dissipation (double dissipation)
Set compliant contact normal dissipation in 1/velocity (s/m, >= 0). More...

void SetStiffnessAndDissipation (double cfm, double erp)
Sets stiffness and dissipation for the rod from cfm and erp values (used for discretized system implementations). More...

double get_mu_static () const
Get compliant contact static friction (stiction) coefficient μ_s. More...

void set_mu_static (double mu_static)
Set contact stiction coefficient (>= mu_coulomb). More...

double get_stiction_speed_tolerance () const
Get the stiction speed tolerance (m/s). More...

void set_stiction_speed_tolerance (double v_stick_tol)
Set the stiction speed tolerance (m/s). More...

Matrix2< T > GetSlidingContactFrameToWorldTransform (const T &xaxis_velocity) const
Gets the rotation matrix that transforms velocities from a sliding contact frame to the global frame. More...

Matrix2< T > GetNonSlidingContactFrameToWorldTransform () const
Gets the rotation matrix that transforms velocities from a non-sliding contact frame to the global frame. More...

bool IsImpacting (const systems::Context< T > &context) const
Checks whether the system is in an impacting state, meaning that the relative velocity along the contact normal between the rod and the halfspace is such that the rod will begin interpenetrating the halfspace at any time Δt in the future (i.e., Δt > 0). More...

double get_integration_step_size () const
Gets the integration step size for the discretized system. More...

SystemType get_system_type () const
Gets the model and simulation type for this system. More...

Vector3< T > CalcCompliantContactForces (const systems::Context< T > &context) const
Return net contact forces as a spatial force F_Ro_W=(fx,fy,τ) where translational force f_Ro_W=(fx,fy) is applied at the rod origin Ro, and torque t_R=τ is the moment due to the contact forces actually being applied elsewhere. More...

int DetermineNumWitnessFunctions (const systems::Context< T > &context) const
Gets the number of witness functions for the system active in the system for a given state (using context). More...

const systems::OutputPort< T > & pose_output () const
Returns the 3D pose of this rod. More...

void GetContactPoints (const systems::Context< T > &context, std::vector< Vector2< T >> *points) const
Gets the point(s) of contact for the 2D rod. More...

void GetContactPointsTangentVelocities (const systems::Context< T > &context, const std::vector< Vector2< T >> &points, std::vector< T > *vels) const
Gets the tangent velocities for all contact points. More...

void CalcConstraintProblemData (const systems::Context< T > &context, const std::vector< Vector2< T >> &points, const std::vector< T > &tangent_vels, multibody::constraint::ConstraintAccelProblemData< T > *data) const
Initializes the contact data for the rod, given a set of contact points. More...

void CalcImpactProblemData (const systems::Context< T > &context, const std::vector< Vector2< T >> &points, multibody::constraint::ConstraintVelProblemData< T > *data) const
Initializes the impacting contact data for the rod, given a set of contact points. More...

Public Member Functions inherited from LeafSystem< T >
~LeafSystem () override

std::unique_ptr< CompositeEventCollection< T > > AllocateCompositeEventCollection () const final
Allocates a CompositeEventCollection object for this system. More...

std::unique_ptr< LeafContext< T > > AllocateContext () const
Shadows System<T>::AllocateContext to provide a more concrete return type LeafContext<T>. More...

std::unique_ptr< ContextBaseDoAllocateContext () const final
Derived class implementations should allocate a suitable concrete Context type, then invoke the above InitializeContextBase() method. More...

void SetDefaultState (const Context< T > &context, State< T > *state) const override
Default implementation: sets all continuous state to the model vector given in DeclareContinuousState (or zero if no model vector was given) and discrete states to zero. More...

void SetDefaultParameters (const Context< T > &context, Parameters< T > *parameters) const override
Default implementation: sets all numeric parameters to the model vector given to DeclareNumericParameter, or else if no model was provided sets the numeric parameter to one. More...

std::unique_ptr< ContinuousState< T > > AllocateTimeDerivatives () const override
Returns the AllocateContinuousState value, which must not be nullptr. More...

std::unique_ptr< DiscreteValues< T > > AllocateDiscreteVariables () const override
Returns the AllocateDiscreteState value, which must not be nullptr. More...

std::multimap< int, intGetDirectFeedthroughs () const final
Reports all direct feedthroughs from input ports to output ports. More...

LeafSystem (const LeafSystem &)=delete

LeafSystemoperator= (const LeafSystem &)=delete

LeafSystem (LeafSystem &&)=delete

LeafSystemoperator= (LeafSystem &&)=delete

Public Member Functions inherited from System< T >
~System () override=default

void GetWitnessFunctions (const Context< T > &context, std::vector< const WitnessFunction< T > * > *w) const
Gets the witness functions active for the given state. More...

CalcWitnessValue (const Context< T > &context, const WitnessFunction< T > &witness_func) const
Evaluates a witness function at the given context. More...

System (const System &)=delete

Systemoperator= (const System &)=delete

System (System &&)=delete

Systemoperator= (System &&)=delete

std::unique_ptr< Context< T > > AllocateContext () const
Returns a Context<T> suitable for use with this System<T>. More...

std::unique_ptr< BasicVector< T > > AllocateInputVector (const InputPort< T > &input_port) const
Given an input port, allocates the vector storage. More...

std::unique_ptr< AbstractValueAllocateInputAbstract (const InputPort< T > &input_port) const
Given an input port, allocates the abstract storage. More...

std::unique_ptr< SystemOutput< T > > AllocateOutput () const
Returns a container that can hold the values of all of this System's output ports. More...

std::unique_ptr< Context< T > > CreateDefaultContext () const
This convenience method allocates a context using AllocateContext() and sets its default values using SetDefaultContext(). More...

void SetDefaultContext (Context< T > *context) const

virtual void SetRandomState (const Context< T > &context, State< T > *state, RandomGenerator *generator) const
Assigns random values to all elements of the state. More...

virtual void SetRandomParameters (const Context< T > &context, Parameters< T > *parameters, RandomGenerator *generator) const
Assigns random values to all parameters. More...

void SetRandomContext (Context< T > *context, RandomGenerator *generator) const

void AllocateFixedInputs (Context< T > *context) const
For each input port, allocates a fixed input of the concrete type that this System requires, and binds it to the port, disconnecting any prior input. More...

bool HasAnyDirectFeedthrough () const
Returns true if any of the inputs to the system might be directly fed through to any of its outputs and false otherwise. More...

bool HasDirectFeedthrough (int output_port) const
Returns true if there might be direct-feedthrough from any input port to the given output_port, and false otherwise. More...

bool HasDirectFeedthrough (int input_port, int output_port) const
Returns true if there might be direct-feedthrough from the given input_port to the given output_port, and false otherwise. More...

void Publish (const Context< T > &context, const EventCollection< PublishEvent< T >> &events) const
This method is the public entry point for dispatching all publish event handlers. More...

void Publish (const Context< T > &context) const
Forces a publish on the system, given a context. More...

const T & EvalConservativePower (const Context< T > &context) const
Returns a reference to the cached value of the conservative power. More...

const T & EvalNonConservativePower (const Context< T > &context) const
Returns a reference to the cached value of the non-conservative power. More...

template<template< typename > class Vec = BasicVector>
const Vec< T > * EvalVectorInput (const Context< T > &context, int port_index) const
Returns the value of the vector-valued input port with the given port_index as a BasicVector or a specific subclass Vec derived from BasicVector. More...

Eigen::VectorBlock< const VectorX< T > > EvalEigenVectorInput (const Context< T > &context, int port_index) const
Returns the value of the vector-valued input port with the given port_index as an Eigen vector. More...

int get_num_constraint_equations (const Context< T > &context) const
Gets the number of constraint equations for this system using the given context (useful in case the number of constraints is dependent upon the current state (as might be the case with a system modeled using piecewise differential algebraic equations). More...

Eigen::VectorXd EvalConstraintEquations (const Context< T > &context) const
Evaluates the constraint equations for the system at the generalized coordinates and generalized velocity specified by the context. More...

Eigen::VectorXd EvalConstraintEquationsDot (const Context< T > &context) const
Computes the time derivative of each constraint equation, evaluated at the generalized coordinates and generalized velocity specified by the context. More...

Eigen::VectorXd CalcVelocityChangeFromConstraintImpulses (const Context< T > &context, const Eigen::MatrixXd &J, const Eigen::VectorXd &lambda) const
Computes the change in velocity from applying the given constraint forces to the system at the given context. More...

double CalcConstraintErrorNorm (const Context< T > &context, const Eigen::VectorXd &error) const
Computes the norm on constraint error (used as a metric for comparing errors between the outputs of algebraic equations applied to two different state variable instances). More...

void CalcTimeDerivatives (const Context< T > &context, ContinuousState< T > *derivatives) const
Calculates the time derivatives xcdot of the continuous state xc. More...

void CalcDiscreteVariableUpdates (const Context< T > &context, const EventCollection< DiscreteUpdateEvent< T >> &events, DiscreteValues< T > *discrete_state) const
This method is the public entry point for dispatching all discrete variable update event handlers. More...

void CalcDiscreteVariableUpdates (const Context< T > &context, DiscreteValues< T > *discrete_state) const
This method forces a discrete update on the system given a context, and the updated discrete state is stored in discrete_state. More...

void CalcUnrestrictedUpdate (const Context< T > &context, const EventCollection< UnrestrictedUpdateEvent< T >> &events, State< T > *state) const
This method is the public entry point for dispatching all unrestricted update event handlers. More...

void CalcUnrestrictedUpdate (const Context< T > &context, State< T > *state) const
This method forces an unrestricted update on the system given a context, and the updated state is stored in state. More...

CalcNextUpdateTime (const Context< T > &context, CompositeEventCollection< T > *events) const
This method is called by a Simulator during its calculation of the size of the next continuous step to attempt. More...

void GetPerStepEvents (const Context< T > &context, CompositeEventCollection< T > *events) const
This method is called by Simulator::Initialize() to gather all update and publish events that are to be handled in StepTo() at the point before Simulator integrates continuous state. More...

void GetInitializationEvents (const Context< T > &context, CompositeEventCollection< T > *events) const
This method is called by Simulator::Initialize() to gather all update and publish events that need to be handled at initialization before the simulator starts integration. More...

optional< PeriodicEventDataGetUniquePeriodicDiscreteUpdateAttribute () const
Gets whether there exists a unique periodic attribute that triggers one or more discrete update events (and, if so, returns that unique periodic attribute). More...

std::map< PeriodicEventData, std::vector< const Event< T > * >, PeriodicEventDataComparatorGetPeriodicEvents () const
Gets all periodic triggered events for a system. More...

void CalcOutput (const Context< T > &context, SystemOutput< T > *outputs) const
Utility method that computes for every output port i the value y(i) that should result from the current contents of the given Context. More...

CalcPotentialEnergy (const Context< T > &context) const
Calculates and returns the potential energy current stored in the configuration provided in context. More...

CalcKineticEnergy (const Context< T > &context) const
Calculates and returns the kinetic energy currently present in the motion provided in the given Context. More...

CalcConservativePower (const Context< T > &context) const
Calculates and returns the rate at which mechanical energy is being converted from potential energy to kinetic energy by this system in the given Context. More...

CalcNonConservativePower (const Context< T > &context) const
Calculates and returns the rate at which mechanical energy is being generated (positive) or dissipated (negative) other than by conversion between potential and kinetic energy (in the given Context). More...

void MapVelocityToQDot (const Context< T > &context, const VectorBase< T > &generalized_velocity, VectorBase< T > *qdot) const
Transforms a given generalized velocity v to the time derivative qdot of the generalized configuration q taken from the supplied Context. More...

void MapVelocityToQDot (const Context< T > &context, const Eigen::Ref< const VectorX< T >> &generalized_velocity, VectorBase< T > *qdot) const
Transforms the given generalized velocity to the time derivative of generalized configuration. More...

void MapQDotToVelocity (const Context< T > &context, const VectorBase< T > &qdot, VectorBase< T > *generalized_velocity) const
Transforms the time derivative qdot of the generalized configuration q to generalized velocities v. More...

void MapQDotToVelocity (const Context< T > &context, const Eigen::Ref< const VectorX< T >> &qdot, VectorBase< T > *generalized_velocity) const
Transforms the given time derivative qdot of generalized configuration q to generalized velocity v. More...

std::string GetMemoryObjectName () const
Returns a name for this System based on a stringification of its type name and memory address. More...

const InputPort< T > & get_input_port (int port_index) const
Returns the typed input port at index port_index. More...

const OutputPort< T > & get_output_port (int port_index) const
Returns the typed output port at index port_index. More...

int get_num_constraints () const
Returns the number of constraints specified for the system. More...

const SystemConstraint< T > & get_constraint (SystemConstraintIndex constraint_index) const
Returns the constraint at index constraint_index. More...

bool CheckSystemConstraintsSatisfied (const Context< T > &context, double tol) const
Returns true if context satisfies all of the registered SystemConstraints with tolerance tol. More...

void CheckValidOutput (const SystemOutput< T > *output) const
Checks that output is consistent with the number and size of output ports declared by the system. More...

template<typename T1 = T>
void CheckValidContextT (const Context< T1 > &context) const
Checks that context is consistent for this System template. More...

VectorX< T > CopyContinuousStateVector (const Context< T > &context) const
Returns a copy of the continuous state vector xc into an Eigen vector. More...

std::string GetGraphvizString () const
Returns a Graphviz string describing this System. More...

int64_t GetGraphvizId () const
Returns an opaque integer that uniquely identifies this system in the Graphviz output. More...

void FixInputPortsFrom (const System< double > &other_system, const Context< double > &other_context, Context< T > *target_context) const
Fixes all of the input ports in target_context to their current values in other_context, as evaluated by other_system. More...

const SystemScalarConverterget_system_scalar_converter () const
(Advanced) Returns the SystemScalarConverter for this object. More...

std::unique_ptr< System< AutoDiffXd > > ToAutoDiffXd () const
Creates a deep copy of this System, transmogrified to use the autodiff scalar type, with a dynamic-sized vector of partial derivatives. More...

std::unique_ptr< System< AutoDiffXd > > ToAutoDiffXdMaybe () const
Creates a deep copy of this system exactly like ToAutoDiffXd(), but returns nullptr if this System does not support autodiff, instead of throwing an exception. More...

std::unique_ptr< System< symbolic::Expression > > ToSymbolic () const
Creates a deep copy of this System, transmogrified to use the symbolic scalar type. More...

std::unique_ptr< System< symbolic::Expression > > ToSymbolicMaybe () const
Creates a deep copy of this system exactly like ToSymbolic(), but returns nullptr if this System does not support symbolic, instead of throwing an exception. More...

Public Member Functions inherited from SystemBase
~SystemBase () override

void set_name (const std::string &name)
Sets the name of the system. More...

const std::string & get_name () const
Returns the name last supplied to set_name(), if any. More...

const std::string & GetSystemName () const final
Returns a human-readable name for this system, for use in messages and logging. More...

std::string GetSystemPathname () const final
Generates and returns a human-readable full path name of this subsystem, for use in messages and logging. More...

std::string GetSystemType () const final
Returns the most-derived type of this concrete System object as a human-readable string suitable for use in error messages. More...

void ThrowIfContextNotCompatible (const ContextBase &context) const final
Throws an exception with an appropriate message if the given context is not compatible with this System. More...

std::unique_ptr< ContextBaseAllocateContext () const
Returns a Context suitable for use with this System. More...

int get_num_input_ports () const
Returns the number of input ports currently allocated in this System. More...

int get_num_output_ports () const
Returns the number of output ports currently allocated in this System. More...

const InputPortBaseget_input_port_base (InputPortIndex port_index) const
Returns a reference to an InputPort given its port_index. More...

const OutputPortBaseget_output_port_base (OutputPortIndex port_index) const
Returns a reference to an OutputPort given its port_index. More...

int get_num_total_inputs () const
Returns the total dimension of all of the vector-valued input ports (as if they were muxed). More...

int get_num_total_outputs () const
Returns the total dimension of all of the vector-valued output ports (as if they were muxed). More...

int num_cache_entries () const
Returns the number nc of cache entries currently allocated in this System. More...

const CacheEntryget_cache_entry (CacheIndex index) const
Return a reference to a CacheEntry given its index. More...

void CheckValidContext (const ContextBase &context) const
Checks whether the given context is valid for this System and throws an exception with a helpful message if not. More...

SystemBase (const SystemBase &)=delete

SystemBaseoperator= (const SystemBase &)=delete

SystemBase (SystemBase &&)=delete

SystemBaseoperator= (SystemBase &&)=delete

const AbstractValueEvalAbstractInput (const ContextBase &context, int port_index) const
Returns the value of the input port with the given port_index as an AbstractValue, which is permitted for ports of any type. More...

template<typename V >
const V * EvalInputValue (const ContextBase &context, int port_index) const
Returns the value of an abstract-valued input port with the given port_index as a value of known type V. More...

const CacheEntryDeclareCacheEntry (std::string description, CacheEntry::AllocCallback alloc_function, CacheEntry::CalcCallback calc_function, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
Declares a new CacheEntry in this System using the least-restrictive definitions for the associated functions. More...

template<class MySystem , class MyContext , typename ValueType >
const CacheEntryDeclareCacheEntry (std::string description, ValueType(MySystem::*make)() const, void(MySystem::*calc)(const MyContext &, ValueType *) const, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
Declares a cache entry by specifying member functions to use both for the allocator and calculator. More...

template<class MySystem , class MyContext , typename ValueType >
const CacheEntryDeclareCacheEntry (std::string description, const ValueType &model_value, void(MySystem::*calc)(const MyContext &, ValueType *) const, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
Declares a cache entry by specifying a model value of concrete type ValueType and a calculator function that is a class member function (method) with signature: More...

template<class MySystem , class MyContext , typename ValueType >
const CacheEntryDeclareCacheEntry (std::string description, void(MySystem::*calc)(const MyContext &, ValueType *) const, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
Declares a cache entry by specifying only a calculator function that is a class member function (method) with signature: More...

DependencyTicket input_port_ticket (InputPortIndex index)
Returns a ticket indicating dependence on the input port indicated by index. More...

DependencyTicket output_port_ticket (OutputPortIndex index)
Returns a ticket indicating dependence on the output port indicated by index. More...

DependencyTicket cache_entry_ticket (CacheIndex index)
Returns a ticket indicating dependence on the cache entry indicated by index. More...

int num_discrete_state_groups () const
Returns the number of declared discrete state groups (each group is a vector-valued discrete state variable). More...

int num_abstract_states () const
Returns the number of declared abstract state variables. More...

int num_numeric_parameters () const
Returns the number of declared numeric parameters (each of these is a vector-valued parameter). More...

int num_abstract_parameters () const
Returns the number of declared abstract parameters. More...

DependencyTicket discrete_state_ticket (DiscreteStateIndex index) const
Returns a ticket indicating dependence on a particular discrete state variable (may be a vector). More...

DependencyTicket abstract_state_ticket (AbstractStateIndex index) const
Returns a ticket indicating dependence on a particular abstract state variable. More...

DependencyTicket numeric_parameter_ticket (NumericParameterIndex index) const
Returns a ticket indicating dependence on a particular numeric parameter (may be a vector). More...

DependencyTicket abstract_parameter_ticket (AbstractParameterIndex index) const
Returns a ticket indicating dependence on a particular abstract parameter. More...

Static Public Member Functions

static const Rod2dStateVector< T > & get_state (const systems::ContinuousState< T > &cstate)

static Rod2dStateVector< T > & get_mutable_state (systems::ContinuousState< T > *cstate)

static const Rod2dStateVector< T > & get_state (const systems::Context< T > &context)

static Rod2dStateVector< T > & get_mutable_state (systems::Context< T > *context)

static Vector2< T > CalcRodEndpoint (const T &x, const T &y, int k, const T &ctheta, const T &stheta, double half_rod_len)
Utility method for determining the World frame location of one of three points on the rod whose origin is Ro. More...

static Vector2< T > CalcCoincidentRodPointVelocity (const Vector2< T > &p_WRo, const Vector2< T > &v_WRo, const T &w_WR, const Vector2< T > &p_WC)
Given a location p_WC of a point C in the World frame, define the point Rc on the rod that is coincident with C, and report Rc's World frame velocity v_WRc. More...

Static Public Member Functions inherited from System< T >
template<template< typename > class S = ::drake::systems::System>
static std::unique_ptr< S< AutoDiffXd > > ToAutoDiffXd (const S< T > &from)
Creates a deep copy of from, transmogrified to use the autodiff scalar type, with a dynamic-sized vector of partial derivatives. More...

template<template< typename > class S = ::drake::systems::System>
static std::unique_ptr< S< symbolic::Expression > > ToSymbolic (const S< T > &from)
Creates a deep copy of from, transmogrified to use the symbolic scalar type. More...

Static Public Member Functions inherited from SystemBase
static DependencyTicket all_sources_ticket ()
Returns a ticket indicating dependence on every possible independent source value, including time, state, input ports, parameters, and the accuracy setting (but not cache entries). More...

static DependencyTicket nothing_ticket ()
Returns a ticket indicating that a computation does not depend on any source value; that is, it is a constant. More...

static DependencyTicket time_ticket ()
Returns a ticket indicating dependence on time. More...

static DependencyTicket accuracy_ticket ()
Returns a ticket indicating dependence on the accuracy setting in the Context. More...

static DependencyTicket q_ticket ()
Returns a ticket indicating that a computation depends on configuration state variables q. More...

static DependencyTicket v_ticket ()
Returns a ticket indicating dependence on velocity state variables v. More...

static DependencyTicket z_ticket ()
Returns a ticket indicating dependence on all of the miscellaneous continuous state variables z. More...

static DependencyTicket xc_ticket ()
Returns a ticket indicating dependence on all of the continuous state variables q, v, or z. More...

static DependencyTicket xd_ticket ()
Returns a ticket indicating dependence on all of the numerical discrete state variables, in any discrete variable group. More...

static DependencyTicket xa_ticket ()
Returns a ticket indicating dependence on all of the abstract state variables in the current Context. More...

static DependencyTicket all_state_ticket ()
Returns a ticket indicating dependence on all state variables x in this system, including continuous variables xc, discrete (numeric) variables xd, and abstract state variables xa. More...

static DependencyTicket xcdot_ticket ()
Returns a ticket for the cache entry that holds time derivatives of the continuous variables. More...

static DependencyTicket xdhat_ticket ()
Returns a ticket for the cache entry that holds the discrete state update for the numerical discrete variables in the state. More...

static DependencyTicket configuration_ticket ()
Returns a ticket indicating dependence on all the configuration variables for this System. More...

static DependencyTicket velocity_ticket ()
(Advanced) Returns a ticket indicating dependence on all of the velocity variables, but not the configuration variables for this System. More...

static DependencyTicket kinematics_ticket ()
Returns a ticket indicating dependence on all of the configuration and velocity state variables of this System. More...

static DependencyTicket all_parameters_ticket ()
Returns a ticket indicating dependence on all parameters p in this system, including numeric parameters pn, and abstract parameters pa. More...

static DependencyTicket all_input_ports_ticket ()
Returns a ticket indicating dependence on all input ports u of this system. More...

Friends

class Rod2DDAETest

class Rod2DDAETest_RigidContactProblemDataBallistic_Test

Protected Member Functions inherited from LeafSystem< T >
LeafSystem ()
Default constructor that declares no inputs, outputs, state, parameters, events, nor scalar-type conversion support (AutoDiff, etc.). More...

LeafSystem (SystemScalarConverter converter)
Constructor that declares no inputs, outputs, state, parameters, or events, but allows subclasses to declare scalar-type conversion support (AutoDiff, etc.). More...

virtual std::unique_ptr< LeafContext< T > > DoMakeLeafContext () const
Provides a new instance of the leaf context for this system. More...

virtual void DoValidateAllocatedLeafContext (const LeafContext< T > &context) const
Derived classes that impose restrictions on what resources are permitted should check those restrictions by implementing this. More...

DoCalcWitnessValue (const Context< T > &context, const WitnessFunction< T > &witness_func) const final
Derived classes will implement this method to evaluate a witness function at the given context. More...

void AddTriggeredWitnessFunctionToCompositeEventCollection (Event< T > *event, CompositeEventCollection< T > *events) const final
Add event to events due to a witness function triggering. More...

void DoCalcNextUpdateTime (const Context< T > &context, CompositeEventCollection< T > *events, T *time) const override
Computes the next update time based on the configured periodic events, for scalar types that are arithmetic, or aborts for scalar types that are not arithmetic. More...

BasicVector< T > * DoAllocateInputVector (const InputPort< T > &input_port) const override
Allocates a vector that is suitable as an input value for input_port. More...

AbstractValueDoAllocateInputAbstract (const InputPort< T > &input_port) const override
Allocates an AbstractValue suitable as an input value for input_port. More...

void GetGraphvizFragment (std::stringstream *dot) const override
Emits a graphviz fragment for this System. More...

void GetGraphvizInputPortToken (const InputPort< T > &port, std::stringstream *dot) const final
Appends a fragment to the dot stream identifying the graphviz node representing port. More...

void GetGraphvizOutputPortToken (const OutputPort< T > &port, std::stringstream *dot) const final
Appends a fragment to the dot stream identifying the graphviz node representing port. More...

virtual std::unique_ptr< ContinuousState< T > > AllocateContinuousState () const
Returns a ContinuousState used to implement both CreateDefaultContext and AllocateTimeDerivatives. More...

virtual std::unique_ptr< DiscreteValues< T > > AllocateDiscreteState () const
Reserves the discrete state as required by CreateDefaultContext. More...

virtual std::unique_ptr< Parameters< T > > AllocateParameters () const
Reserves the parameters as required by CreateDefaultContext. More...

virtual optional< boolDoHasDirectFeedthrough (int input_port, int output_port) const
Returns true if there is direct-feedthrough from the given input_port to the given output_port, false if there is not direct-feedthrough, or nullopt if unknown (in which case SystemSymbolicInspector will attempt to measure the feedthrough using symbolic form). More...

int DeclareNumericParameter (const BasicVector< T > &model_vector)
Declares a numeric parameter using the given model_vector. More...

template<template< typename > class U = BasicVector>
const U< T > & GetNumericParameter (const Context< T > &context, int index) const
Extracts the numeric parameters of type U from the context at index. More...

template<template< typename > class U = BasicVector>
U< T > & GetMutableNumericParameter (Context< T > *context, int index) const
Extracts the numeric parameters of type U from the context at index. More...

int DeclareAbstractParameter (const AbstractValue &model_value)
Declares an abstract parameter using the given model_value. More...

template<typename EventType >
void DeclarePeriodicEvent (double period_sec, double offset_sec)
Declares that this System has a simple, fixed-period event specified with no custom callback function, and its attribute field contains an Event<T>::PeriodicAttribute constructed from the specified period_sec and offset_sec. More...

template<typename EventType >
void DeclarePeriodicEvent (double period_sec, double offset_sec, const EventType &event)
Declares that this System has a simple, fixed-period event specified by event. More...

void DeclarePeriodicDiscreteUpdate (double period_sec, double offset_sec=0)
Declares a periodic discrete update event with period = period_sec and offset = offset_sec. More...

void DeclarePeriodicUnrestrictedUpdate (double period_sec, double offset_sec=0)
Declares a periodic unrestricted update event with period = period_sec and offset = offset_sec. More...

void DeclarePeriodicPublish (double period_sec, double offset_sec=0)
Declares a periodic publish event with period = period_sec and offset = offset_sec. More...

template<typename EventType >
void DeclarePerStepEvent (const EventType &event)
Declares a per-step event using event, which is deep copied (the copy is maintained by this). More...

template<typename EventType >
void DeclareInitializationEvent (const EventType &event)
Declares an initialization event by deep copying event and storing it internally. More...

void DeclareContinuousState (int num_state_variables)
Declares that this System should reserve continuous state with num_state_variables state variables, which have no second-order structure. More...

void DeclareContinuousState (int num_q, int num_v, int num_z)
Declares that this System should reserve continuous state with num_q generalized positions, num_v generalized velocities, and num_z miscellaneous state variables. More...

void DeclareContinuousState (const BasicVector< T > &model_vector)
Declares that this System should reserve continuous state with model_vector.size() miscellaneous state variables, stored in a vector Cloned from model_vector. More...

void DeclareContinuousState (const BasicVector< T > &model_vector, int num_q, int num_v, int num_z)
Declares that this System should reserve continuous state with num_q generalized positions, num_v generalized velocities, and num_z miscellaneous state variables, stored in a vector Cloned from model_vector. More...

void DeclareContinuousState (std::unique_ptr< BasicVector< T >> model_vector, int num_q, int num_v, int num_z)
Declares that this System should reserve continuous state with num_q generalized positions, num_v generalized velocities, and num_z miscellaneous state variables, stored in the a vector Cloned from model_vector. More...

void DeclareDiscreteState (int num_state_variables)
Declares that this System should reserve discrete state with num_state_variables state variables. More...

int DeclareAbstractState (std::unique_ptr< AbstractValue > abstract_state)
Declares an abstract state. More...

template<class MySystem >
SystemConstraintIndex DeclareEqualityConstraint (void(MySystem::*calc)(const Context< T > &, VectorX< T > *) const, int count, const std::string &description)
Declares a system constraint of the form f(context) = 0 by specifying a member function to use to calculate the (VectorX) constraint value with a signature: More...

SystemConstraintIndex DeclareEqualityConstraint (typename SystemConstraint< T >::CalcCallback calc, int count, const std::string &description)
Declares a system constraint of the form f(context) = 0 by specifying a std::function to use to calculate the (Vector) constraint value with a signature: More...

template<class MySystem >
SystemConstraintIndex DeclareInequalityConstraint (void(MySystem::*calc)(const Context< T > &, VectorX< T > *) const, int count, const std::string &description)
Declares a system constraint of the form f(context) ≥ 0 by specifying a member function to use to calculate the (VectorX) constraint value with a signature: More...

SystemConstraintIndex DeclareInequalityConstraint (typename SystemConstraint< T >::CalcCallback calc, int count, const std::string &description)
Declares a system constraint of the form f(context) ≥ 0 by specifying a std::function to use to calculate the (Vector) constraint value with a signature: More...

virtual void DoPublish (const Context< T > &context, const std::vector< const PublishEvent< T > * > &events) const
Derived-class event handler for all simultaneous publish events in events. More...

virtual void DoCalcDiscreteVariableUpdates (const Context< T > &context, const std::vector< const DiscreteUpdateEvent< T > * > &events, DiscreteValues< T > *discrete_state) const
Derived-class event handler for all simultaneous discrete update events. More...

virtual void DoCalcUnrestrictedUpdate (const Context< T > &context, const std::vector< const UnrestrictedUpdateEvent< T > * > &events, State< T > *state) const
Derived-class event handler for all simultaneous unrestricted update events. More...

const InputPort< T > & DeclareVectorInputPort (const BasicVector< T > &model_vector, optional< RandomDistribution > random_type=nullopt)
Declares a vector-valued input port using the given model_vector. More...

const InputPort< T > & DeclareAbstractInputPort (const AbstractValue &model_value)
Declares an abstract-valued input port using the given model_value. More...

template<class MySystem >
std::unique_ptr< WitnessFunction< T > > DeclareWitnessFunction (const std::string &description, const WitnessFunctionDirection &direction_type, T(MySystem::*calc)(const Context< T > &) const) const
Constructs the witness function with the given description (used primarily for debugging and logging), direction type, and calculator function; and with no event object. More...

std::unique_ptr< WitnessFunction< T > > DeclareWitnessFunction (const std::string &description, const WitnessFunctionDirection &direction_type, std::function< T(const Context< T > &)> calc) const
Constructs the witness function with the given description (used primarily for debugging and logging), direction type, and calculator function; and with no event object. More...

template<class MySystem >
std::unique_ptr< WitnessFunction< T > > DeclareWitnessFunction (const std::string &description, const WitnessFunctionDirection &direction_type, T(MySystem::*calc)(const Context< T > &) const, void(MySystem::*publish_callback)(const Context< T > &, const PublishEvent< T > &) const) const
Constructs the witness function with the given description (used primarily for debugging and logging), direction type, calculator function, and publish event callback function for when this triggers. More...

template<class MySystem >
std::unique_ptr< WitnessFunction< T > > DeclareWitnessFunction (const std::string &description, const WitnessFunctionDirection &direction_type, T(MySystem::*calc)(const Context< T > &) const, void(MySystem::*du_callback)(const Context< T > &, const DiscreteUpdateEvent< T > &, DiscreteValues< T > *) const) const
Constructs the witness function with the given description (used primarily for debugging and logging), direction type, calculator function, and discrete update event callback function for when this triggers. More...

template<class MySystem >
std::unique_ptr< WitnessFunction< T > > DeclareWitnessFunction (const std::string &description, const WitnessFunctionDirection &direction_type, T(MySystem::*calc)(const Context< T > &) const, void(MySystem::*uu_callback)(const Context< T > &, const UnrestrictedUpdateEvent< T > &, State< T > *) const) const
Constructs the witness function with the given description (used primarily for debugging and logging), direction type, calculator function, and unrestricted update event callback function for when this triggers. More...

template<class MySystem >
std::unique_ptr< WitnessFunction< T > > DeclareWitnessFunction (const std::string &description, const WitnessFunctionDirection &direction_type, T(MySystem::*calc)(const Context< T > &) const, const Event< T > &e) const
Constructs the witness function with the given description (used primarily for debugging and logging), direction type, and calculator function, and with an object corresponding to the event that is to be dispatched when this witness function triggers. More...

std::unique_ptr< WitnessFunction< T > > DeclareWitnessFunction (const std::string &description, const WitnessFunctionDirection &direction_type, std::function< T(const Context< T > &)> calc, const Event< T > &e) const
Constructs the witness function with the given description (used primarily for debugging and logging), direction type, and calculator function, and with an object corresponding to the event that is to be dispatched when this witness function triggers. More...

template<class MySystem , typename BasicVectorSubtype >
const OutputPort< T > & DeclareVectorOutputPort (const BasicVectorSubtype &model_vector, void(MySystem::*calc)(const Context< T > &, BasicVectorSubtype *) const, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
Declares a vector-valued output port by specifying (1) a model vector of type BasicVectorSubtype derived from BasicVector and initialized to the correct size and desired initial value, and (2) a calculator function that is a class member function (method) with signature: More...

template<class MySystem , typename BasicVectorSubtype >
const OutputPort< T > & DeclareVectorOutputPort (void(MySystem::*calc)(const Context< T > &, BasicVectorSubtype *) const, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
Declares a vector-valued output port by specifying only a calculator function that is a class member function (method) with signature: More...

const OutputPort< T > & DeclareVectorOutputPort (const BasicVector< T > &model_vector, typename LeafOutputPort< T >::CalcVectorCallback vector_calc_function, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
(Advanced) Declares a vector-valued output port using the given model_vector and a function for calculating the port's value at runtime. More...

template<class MySystem , typename OutputType >
const OutputPort< T > & DeclareAbstractOutputPort (const OutputType &model_value, void(MySystem::*calc)(const Context< T > &, OutputType *) const, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
Declares an abstract-valued output port by specifying a model value of concrete type OutputType and a calculator function that is a class member function (method) with signature: More...

template<class MySystem , typename OutputType >
const OutputPort< T > & DeclareAbstractOutputPort (void(MySystem::*calc)(const Context< T > &, OutputType *) const, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
Declares an abstract-valued output port by specifying only a calculator function that is a class member function (method) with signature: More...

template<class MySystem , typename OutputType >
const OutputPort< T > & DeclareAbstractOutputPort (OutputType(MySystem::*make)() const, void(MySystem::*calc)(const Context< T > &, OutputType *) const, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
Declares an abstract-valued output port by specifying member functions to use both for the allocator and calculator. More...

const OutputPort< T > & DeclareAbstractOutputPort (typename LeafOutputPort< T >::AllocCallback alloc_function, typename LeafOutputPort< T >::CalcCallback calc_function, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
(Advanced) Declares an abstract-valued output port using the given allocator and calculator functions provided in their most generic forms. More...

Protected Member Functions inherited from System< T >
virtual void DoGetWitnessFunctions (const Context< T > &, std::vector< const WitnessFunction< T > * > *) const
Derived classes can override this method to provide witness functions active for the given state. More...

SystemConstraintIndex AddConstraint (std::unique_ptr< SystemConstraint< T >> constraint)
Adds an already-created constraint to the list of constraints for this System. More...

const EventCollection< PublishEvent< T > > & get_forced_publish_events () const

const EventCollection< DiscreteUpdateEvent< T > > & get_forced_discrete_update_events () const

const EventCollection< UnrestrictedUpdateEvent< T > > & get_forced_unrestricted_update_events () const

void set_forced_publish_events (std::unique_ptr< EventCollection< PublishEvent< T >>> forced)

void set_forced_discrete_update_events (std::unique_ptr< EventCollection< DiscreteUpdateEvent< T >>> forced)

void set_forced_unrestricted_update_events (std::unique_ptr< EventCollection< UnrestrictedUpdateEvent< T >>> forced)

System (SystemScalarConverter converter)
Constructs an empty System base class object, possibly supporting scalar-type conversion support (AutoDiff, etc.) using converter. More...

const InputPort< T > & DeclareInputPort (PortDataType type, int size, optional< RandomDistribution > random_type=nullopt)
Adds a port with the specified type and size to the input topology. More...

const InputPort< T > & DeclareAbstractInputPort ()
Adds an abstract-valued port to the input topology. More...

virtual void DoCalcTimeDerivatives (const Context< T > &context, ContinuousState< T > *derivatives) const
Override this if you have any continuous state variables xc in your concrete System to calculate their time derivatives. More...

virtual T DoCalcPotentialEnergy (const Context< T > &context) const
Override this method for physical systems to calculate the potential energy currently stored in the configuration provided in the given Context. More...

virtual T DoCalcKineticEnergy (const Context< T > &context) const
Override this method for physical systems to calculate the kinetic energy currently present in the motion provided in the given Context. More...

virtual T DoCalcConservativePower (const Context< T > &context) const
Override this method to return the rate at which mechanical energy is being converted from potential energy to kinetic energy by this system in the given Context. More...

virtual T DoCalcNonConservativePower (const Context< T > &context) const
Override this method to return the rate at which mechanical energy is being generated (positive) or dissipated (negative) other than by conversion between potential and kinetic energy (in the given Context). More...

virtual void DoMapQDotToVelocity (const Context< T > &context, const Eigen::Ref< const VectorX< T >> &qdot, VectorBase< T > *generalized_velocity) const
Provides the substantive implementation of MapQDotToVelocity(). More...

virtual void DoMapVelocityToQDot (const Context< T > &context, const Eigen::Ref< const VectorX< T >> &generalized_velocity, VectorBase< T > *qdot) const
Provides the substantive implementation of MapVelocityToQDot(). More...

virtual int do_get_num_constraint_equations (const Context< T > &context) const
Gets the number of constraint equations for this system from the given context. More...

virtual Eigen::VectorXd DoEvalConstraintEquations (const Context< T > &context) const
Evaluates the constraint equations for the system at the generalized coordinates and generalized velocity specified by the context. More...

virtual Eigen::VectorXd DoEvalConstraintEquationsDot (const Context< T > &context) const
Computes the time derivative of each constraint equation, evaluated at the generalized coordinates and generalized velocity specified by the context. More...

virtual Eigen::VectorXd DoCalcVelocityChangeFromConstraintImpulses (const Context< T > &context, const Eigen::MatrixXd &J, const Eigen::VectorXd &lambda) const
Computes the change in velocity from applying the given constraint forces to the system at the given context. More...

virtual double DoCalcConstraintErrorNorm (const Context< T > &context, const Eigen::VectorXd &error) const
Computes the norm of the constraint error. More...

Eigen::VectorBlock< VectorX< T > > GetMutableOutputVector (SystemOutput< T > *output, int port_index) const
Returns a mutable Eigen expression for a vector valued output port with index port_index in this system. More...

Protected Member Functions inherited from SystemBase
SystemBase ()=default
(Internal use only) Default constructor. More...

void AddInputPort (std::unique_ptr< InputPortBase > port)
(Internal use only) Adds an already-constructed input port to this System. More...

void AddOutputPort (std::unique_ptr< OutputPortBase > port)
(Internal use only) Adds an already-constructed output port to this System. More...

(Internal use only) Assigns a ticket to a new discrete variable group with the given index. More...

(Internal use only) Assigns a ticket to a new abstract state variable with the given index. More...

(Internal use only) Assigns a ticket to a new numeric parameter with the given index. More...

(Internal use only) Assigns a ticket to a new abstract parameter with the given index. More...

const CacheEntryDeclareCacheEntryWithKnownTicket (DependencyTicket known_ticket, std::string description, CacheEntry::AllocCallback alloc_function, CacheEntry::CalcCallback calc_function, std::set< DependencyTicket > prerequisites_of_calc={all_sources_ticket()})
(Internal use only) This is for cache entries associated with pre-defined tickets, for example the cache entry for time derivatives. More...

const internal::SystemParentServiceInterface * get_parent_service () const
Returns a pointer to the service interface of the immediately enclosing Diagram if one has been set, otherwise nullptr. More...

DependencyTicket assign_next_dependency_ticket ()
(Internal use only) Assigns the next unused dependency ticket number, unique only within a particular system. More...

const AbstractValueEvalAbstractInputImpl (const char *func, const ContextBase &context, InputPortIndex port_index) const
(Internal use only) Shared code for updating an input port and returning a pointer to its abstract value, or nullptr if the port is not connected. More...

void ThrowNegativePortIndex (const char *func, int port_index) const
Throws std::out_of_range to report a negative port_index that was passed to API method func. More...

void ThrowInputPortIndexOutOfRange (const char *func, InputPortIndex port_index) const
Throws std::out_of_range to report bad input port_index that was passed to API method func. More...

void ThrowOutputPortIndexOutOfRange (const char *func, OutputPortIndex port_index) const
Throws std::out_of_range to report bad output port_index that was passed to API method func. More...

void ThrowNotAVectorInputPort (const char *func, InputPortIndex port_index) const
Throws std::logic_error because someone misused API method func, that is only allowed for declared-vector input ports, on an abstract port whose index is given here. More...

void ThrowInputPortHasWrongType (const char *func, InputPortIndex port_index, const std::string &expected_type, const std::string &actual_type) const
Throws std::logic_error because someone called API method func claiming the input port had some value type that was wrong. More...

void ThrowCantEvaluateInputPort (const char *func, InputPortIndex port_index) const
Throws std::logic_error because someone called API method func, that requires this input port to be evaluatable, but the port was neither fixed nor connected. More...

const InputPortBaseGetInputPortBaseOrThrow (const char *func, int port_index) const
(Internal use only) Returns the InputPortBase at index port_index, throwing std::out_of_range we don't like the port index. More...

const OutputPortBaseGetOutputPortBaseOrThrow (const char *func, int port_index) const
(Internal use only) Returns the OutputPortBase at index port_index, throwing std::out_of_range we don't like the port index. More...

void InitializeContextBase (ContextBase *context) const
This method must be invoked from within derived class DoAllocateContext() implementations right after the concrete Context object has been allocated. More...

Static Protected Member Functions inherited from SystemBase
static void set_parent_service (SystemBase *child, const internal::SystemParentServiceInterface *parent_service)
(Internal use only) Declares that parent_service is the service interface of the Diagram that owns this subsystem. More...

Detailed Description

template<typename T> class drake::examples::rod2d::Rod2D< T >

Dynamical system representation of a rod contacting a half-space in two dimensions.

Notation

In the discussion below and in code comments, we will use the 2D analog of our standard multibody notation as described in detail here: Terminology and Notation.

For a quick summary and translation to 2D:

• When we combine rotational and translational quantities into a single quantity in 3D, we call those "spatial" quantities. In 2D those combined quantities are actually planar, but we will continue to refer to them as "spatial" to keep the notation analogous and promote easy extension of 2D pedagogical examples to 3D.
• We use capital letters to represent bodies and coordinate frames. Frame F has an origin point Fo, and a basis formed by orthogonal unit vector axes Fx and Fy, with an implicit Fz=Fx × Fy always pointing out of the screen for a 2D system. The inertial frame World is W, and the rod frame is R.
• We also use capitals to represent points, and we allow a frame name F to be used where a point is expected to represent its origin Fo.
• We use p_CD to represent the position vector from point C to point D. Note that if A and B are frames, p_AB means p_AoBo.
• If we need to be explicit about the expressed-in frame F for any quantity, we add the suffix _F to its symbol. So the position vector from C to D, expressed in W, is p_CD_W.
• R_AB is the rotation matrix giving frame B's orientation in frame A.
• X_AB is the transformation matrix giving frame B's pose in frame A, combining both a rotation and a translation; this is conventionally called a "transform". A transform is a spatial quantity.

In 2D, with frames A and B the above quantities are (conceptually) matrices with the indicated dimensions:

    p_AB = Bo-Ao = |x|      R_AB=| cθ -sθ |       X_AB=| R_AB p_AB |
|y|₂ₓ₁        | sθ  cθ |₂ₓ₂         | 0  0   1  |₃ₓ₃


where x,y are B's Cartesian coordinates in the A frame, and θ is the counterclockwise angle from Ax to Bx, measured about Az (and Bz). In practice, 2D rotations are represented just by the scalar angle θ, and 2D transforms are represented by (x,y,θ).

We use v for translational velocity of a point and w (ω) for rotational velocity of a frame. The symbols are:

• v_AP is point P's velocity in frame A, expressed in frame A if no other frame is given as a suffix.
• w_AB is frame B's angular velocity in frame A, expressed in frame A if no other frame is given as a suffix.
• V_AB is frame B's spatial velocity in A, meaning v_ABo and w_AB.

These quantities are conceptually:

    v_AB = |vx|      w_AB=|0|       V_AB=| w_AB |
|vy|           |0|            | v_AB |₆ₓ₁
| 0|₃ₓ₁        |ω|₃ₓ₁


but in 2D we represent translational velocity with just (vx,vy), angular velocity with just the scalar w=ω= $$\dot{\theta}$$ (that is, d/dt θ), and spatial velocity as (vx,vy,ω).

Forces f and torques τ are represented similarly:

• f_P is an in-plane force applied to a point P fixed to some rigid body.
• t_A is an in-plane torque applied to frame A (meaning it is about Az).
• F_A is a spatial force including both f_Ao and t_A.

The above symbols can be suffixed with an expressed-in frame if the frame is not already obvious, so F_A_W is a spatial force applied to frame A (at Ao) but expressed in W. These quantities are conceptually:

    f_A = |fx|      t_A=|0|       F_A=| t_A |
|fy|          |0|           | f_A |₆ₓ₁
| 0|₃ₓ₁       |τ|₃ₓ₁


but in 2D we represent translational force with just (fx,fy), torque with just the scalar t=τ, and spatial force as (fx,fy,τ).

The 2D rod model

The rod's coordinate frame R is placed at the rod's center point Ro, which is also its center of mass Rcm. R's planar pose is given by a planar transform X_WR=(x,y,θ). When X_WR=0 (identity transform), R is coincident with the World frame W, and aligned horizontally as shown:

       +Wy                                  +Ry
|                                    |
|                                    |<---- h ----->
|                      ==============|==============
Wo*-----> +Wx         Rl*            Ro*-----> +Rx    *Rr
=============================
World frame                      Rod R, θ=0


θ is the angle between Rx and Wx, measured using the right hand rule about Wz (out of the screen), that is, counterclockwise. The rod has half-length h, and "left" and "right" endpoints Rl=Ro-h*Rx and Rr=Ro+h*Rx at which it can contact the halfspace whose surface is at Wy=0.

This system can be simulated using one of three models:

• continuously, using a compliant contact model (the rod is rigid, but contact between the rod and the half-space is modeled as compliant) simulated using ordinary differential equations (ODEs),
• a fully rigid model simulated with piecewise differential algebraic equations (DAEs), and
• a fully rigid model simulated as a discrete system using a first-order discretization approach.

The rod state is initialized to the configuration that corresponds to the Painlevé Paradox problem, described in [Stewart 2000]. The paradox consists of a rod contacting a planar surface without impact and subject to sliding Coulomb friction. The problem is well known to correspond to an inconsistent rigid contact configuration*, where impulsive forces are necessary to resolve the problem.

This class uses Drake's -inl.h pattern. When seeing linker errors from this class, please refer to http://drake.mit.edu/cxx_inl.html.

Template Parameters
 T The vector element type, which must be a valid Eigen scalar.

Instantiated templates for the following scalar types T are provided:

• double

Inputs: planar force (two-dimensional) and torque (scalar), which are arbitrary "external" forces (expressed in the world frame) applied at the center-of-mass of the rod.

States: planar position (state indices 0 and 1) and orientation (state index 2), and planar linear velocity (state indices 3 and 4) and scalar angular velocity (state index 5) in units of m, radians, m/s, and rad/s, respectively. Orientation is measured counter- clockwise with respect to the x-axis.

Outputs: Output Port 0 corresponds to the state vector; Output Port 1 corresponds to a PoseVector giving the 3D pose of the rod in the world frame.

• [Stewart, 2000] D. Stewart, "Rigid-Body Dynamics with Friction and Impact". SIAM Rev., 42(1), 3-39, 2000.

Member Enumeration Documentation

 enum SystemType
strong

System model and approach for simulating the system.

Enumerator
kPiecewiseDAE

For modeling the system using rigid contact, Coulomb friction, and hybrid mode variables and simulating the system through piecewise solutions of differential algebraic equations.

kDiscretized

For modeling the system using either rigid or compliant contact, Coulomb friction, and a first-order time discretization (which can be applied to simulating the system without an integrator).

kContinuous

For modeling the system using compliant contact, Coulomb friction, and ordinary differential equations and simulating the system through standard algorithms for solving initial value problems.

Constructor & Destructor Documentation

 ~Rod2D ( )
inlineoverride
 Rod2D ( SystemType system_type, double dt )
explicit

Constructor for the 2D rod system using the piecewise DAE (differential algebraic equation) based approach, the discretization approach, or the continuous ordinary differential equation based approach.

Parameters
 dt The integration step size. This step size cannot be reset after construction.
Exceptions
 std::logic_error if dt is not positive and system_type is kDiscretized or dt is not zero and system_type is kPiecewiseDAE or kContinuous.

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Member Function Documentation

 Vector2< T > CalcCoincidentRodPointVelocity ( const Vector2< T > & p_WRo, const Vector2< T > & v_WRo, const T & w_WR, const Vector2< T > & p_WC )
static

Given a location p_WC of a point C in the World frame, define the point Rc on the rod that is coincident with C, and report Rc's World frame velocity v_WRc.

We're given p_WRo=(x,y) and V_WRo = (v_WRo,w_WR) = (xdot,ydot,thetadot).

Parameters
 p_WRo The center-of-mass of the rod, expressed in the world frame. v_WRo The translational velocity of the rod, expressed in the world frame. w_WR The angular velocity of the rod. p_WC The location of a point on the rod.
Returns
The translational velocity of p_WC, expressed in the world frame.

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 Vector3< T > CalcCompliantContactForces ( const systems::Context< T > & context ) const

Return net contact forces as a spatial force F_Ro_W=(fx,fy,τ) where translational force f_Ro_W=(fx,fy) is applied at the rod origin Ro, and torque t_R=τ is the moment due to the contact forces actually being applied elsewhere.

The returned spatial force may be the resultant of multiple active contact points. Only valid for simulation type kContinuous.

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 void CalcConstraintProblemData ( const systems::Context< T > & context, const std::vector< Vector2< T >> & points, const std::vector< T > & tangent_vels, multibody::constraint::ConstraintAccelProblemData< T > * data ) const

Initializes the contact data for the rod, given a set of contact points.

Aborts if data is null or if points.size() != tangent_vels.size().

Parameters
 points a vector of contact points, expressed in the world frame. tangent_vels a vector of tangent velocities at the contact points, measured along the positive x-axis. [out] data the rigid contact problem data.

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 void CalcImpactProblemData ( const systems::Context< T > & context, const std::vector< Vector2< T >> & points, multibody::constraint::ConstraintVelProblemData< T > * data ) const

Initializes the impacting contact data for the rod, given a set of contact points.

Aborts if data is null.

Parameters
 points a vector of contact points, expressed in the world frame. [out] data the rigid impact problem data.

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 Vector2< T > CalcRodEndpoint ( const T & x, const T & y, int k, const T & ctheta, const T & stheta, double half_rod_len )
static

Utility method for determining the World frame location of one of three points on the rod whose origin is Ro.

Let r be the half-length of the rod. Define point P = Ro+k*r where k = { -1, 0, 1 }. This returns p_WP.

Parameters
 x The horizontal location of the rod center of mass (expressed in the world frame). y The vertical location of the rod center of mass (expressed in the world frame). k The rod endpoint (k=+1 indicates the rod "right" endpoint, k=-1 indicates the rod "left" endpoint, and k=0 indicates the rod origin; each of these are described in the primary class documentation. ctheta cos(theta), where θ is the orientation of the rod (as described in the primary class documentation). stheta sin(theta), where θ is the orientation of the rod (as described in the class documentation). half_rod_len Half the length of the rod.
Returns
p_WP, the designated point on the rod, expressed in the world frame.

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 int DetermineNumWitnessFunctions ( const systems::Context< T > & context ) const

Gets the number of witness functions for the system active in the system for a given state (using context).

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 double get_cfm ( ) const
inline

Gets the constraint force mixing parameter (CFM, used for discretized systems only), which should lie in the interval [0, infinity].

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 double get_dissipation ( ) const
inline

Get compliant contact normal dissipation in 1/velocity (s/m).

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 double get_erp ( ) const
inline

Gets the error reduction parameter (ERP, used for discretized systems only), which should lie in the interval [0, 1].

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 double get_gravitational_acceleration ( ) const
inline

Gets the acceleration (with respect to the positive y-axis) due to gravity (i.e., this number should generally be negative).

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 double get_integration_step_size ( ) const
inline

Gets the integration step size for the discretized system.

Returns
0 if this is a DAE-based system.
 double get_mu_coulomb ( ) const
inline

Gets the coefficient of dynamic (sliding) Coulomb friction.

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 double get_mu_static ( ) const
inline

Get compliant contact static friction (stiction) coefficient μ_s.

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 static Rod2dStateVector& get_mutable_state ( systems::ContinuousState< T > * cstate )
inlinestatic

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 static Rod2dStateVector& get_mutable_state ( systems::Context< T > * context )
inlinestatic
 double get_rod_half_length ( ) const
inline

Gets the half-length h of the rod.

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 double get_rod_mass ( ) const
inline

Gets the mass of the rod.

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 double get_rod_moment_of_inertia ( ) const
inline

Gets the rod moment of inertia.

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 static const Rod2dStateVector& get_state ( const systems::ContinuousState< T > & cstate )
inlinestatic
 static const Rod2dStateVector& get_state ( const systems::Context< T > & context )
inlinestatic
 double get_stiction_speed_tolerance ( ) const
inline

Get the stiction speed tolerance (m/s).

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 double get_stiffness ( ) const
inline

Get compliant contact normal stiffness in N/m.

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 SystemType get_system_type ( ) const
inline

Gets the model and simulation type for this system.

 void GetContactPoints ( const systems::Context< T > & context, std::vector< Vector2< T >> * points ) const

Gets the point(s) of contact for the 2D rod.

context The context storing the current configuration and velocity of the rod. points Contains the contact points (those rod endpoints touching or lying within the ground halfspace) on return. This function aborts if points is null or points is non-empty.

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 void GetContactPointsTangentVelocities ( const systems::Context< T > & context, const std::vector< Vector2< T >> & points, std::vector< T > * vels ) const

Gets the tangent velocities for all contact points.

context The context storing the current configuration and velocity of the rod. points The set of context points. vels Contains the velocities (measured along the x-axis) on return. This function aborts if vels is null. vels will be resized appropriately (to the same number of elements as points) on return.

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 Matrix2< T > GetNonSlidingContactFrameToWorldTransform ( ) const

Gets the rotation matrix that transforms velocities from a non-sliding contact frame to the global frame.

Note: all such non-sliding frames are identical for this example.

Returns
a 2x2 orthogonal matrix with first column set to the contact normal, which is +y ([0 1]) and second column set to the contact tangent +x ([1 0]). Both directions are expressed in the global frame.

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 Vector3 GetRodConfig ( const systems::Context< T > & context ) const
inline

Gets the generalized position of the rod, given a Context.

The first two components represent the location of the rod's center-of-mass, expressed in the global frame. The third component represents the orientation of the rod, measured counter-clockwise with respect to the x-axis.

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 Vector3 GetRodVelocity ( const systems::Context< T > & context ) const
inline

Gets the generalized velocity of the rod, given a Context.

The first two components represent the translational velocities of the center-of-mass. The third component represents the angular velocity of the rod.

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 Matrix2< T > GetSlidingContactFrameToWorldTransform ( const T & xaxis_velocity ) const

Gets the rotation matrix that transforms velocities from a sliding contact frame to the global frame.

Parameters
 xaxis_velocity The velocity of the rod at the point of contact, projected along the +x-axis.
Returns
a 2x2 orthogonal matrix with first column set to the contact normal, which is +y ([0 1]) and second column set to the direction of sliding motion, ±x (±[1 0]). Both directions are expressed in the global frame.
Note
Aborts if xaxis_velocity is zero.

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 bool IsImpacting ( const systems::Context< T > & context ) const

Checks whether the system is in an impacting state, meaning that the relative velocity along the contact normal between the rod and the halfspace is such that the rod will begin interpenetrating the halfspace at any time Δt in the future (i.e., Δt > 0).

If the context does not correspond to a configuration where the rod and halfspace are contacting, this method returns false.

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 const systems::OutputPort& pose_output ( ) const
inline

Returns the 3D pose of this rod.

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 void set_dissipation ( double dissipation )
inline

Set compliant contact normal dissipation in 1/velocity (s/m, >= 0).

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 void set_gravitational_acceleration ( double g )
inline

Sets the acceleration (with respect to the positive y-axis) due to gravity (i.e., this number should generally be negative).

 void set_mu_coulomb ( double mu )
inline

Sets the coefficient of dynamic (sliding) Coulomb friction.

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 void set_mu_static ( double mu_static )
inline

Set contact stiction coefficient (>= mu_coulomb).

This has no effect if the rod model is discretized.

 void set_rod_half_length ( double half_length )
inline

Sets the half-length h of the rod.

 void set_rod_mass ( double mass )
inline

Sets the mass of the rod.

 void set_rod_moment_of_inertia ( double J )
inline

Sets the rod moment of inertia.

 void set_stiction_speed_tolerance ( double v_stick_tol )
inline

Set the stiction speed tolerance (m/s).

This is the maximum slip speed that we are willing to consider as sticking. For a given normal force N this is the speed at which the friction force will be largest, at μ_s*N where μ_s is the static coefficient of friction. This has no effect if the rod model is not compliant.

 void set_stiffness ( double stiffness )
inline

Set compliant contact normal stiffness in N/m (>= 0).

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 void SetStiffnessAndDissipation ( double cfm, double erp )
inline

Sets stiffness and dissipation for the rod from cfm and erp values (used for discretized system implementations).

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 double TransformDampingToDissipationAboutDeformation ( double characteristic_deformation, double b ) const
inline

Transforms damping (b) to dissipation (α) , given a characteristic deformation.

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 double TransformDissipationToDampingAboutDeformation ( double characteristic_deformation ) const
inline

Transforms dissipation (α) to damping, given a characteristic.

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Friends And Related Function Documentation

 friend class Rod2DDAETest
friend
 friend class Rod2DDAETest_RigidContactProblemDataBallistic_Test
friend

The documentation for this class was generated from the following files: